A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling
In machine learning, the processing of datasets is an unavoidable topic. One important approach to solving this problem is to design some corresponding algorithms so that they can eventually converge to the optimal solution of the optimization problem. Most existing acceleration algorithms exhibit a...
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| Format: | Article |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| author | Xuehui Mei Pengrui Zhang Haijun Jiang Zhiyong Yu |
| author_facet | Xuehui Mei Pengrui Zhang Haijun Jiang Zhiyong Yu |
| author_sort | Xuehui Mei |
| collection | DOAJ |
| description | In machine learning, the processing of datasets is an unavoidable topic. One important approach to solving this problem is to design some corresponding algorithms so that they can eventually converge to the optimal solution of the optimization problem. Most existing acceleration algorithms exhibit asymptotic convergence. In order to ensure that the optimization problem converges to the optimal solution within the prescribed time, a novel prescribed-time convergence acceleration algorithm with time rescaling is presented in this paper. Two prescribed-time acceleration algorithms are constructed by introducing time rescaling, and the acceleration algorithms are used to solve unconstrained optimization problems and optimization problems containing equation constraints. Some important theorems are given, and the convergence of the acceleration algorithms is proven using the Lyapunov function method. Finally, we provide numerical simulations to verify the effectiveness and rationality of our theoretical results. |
| format | Article |
| id | doaj-art-5e6ca8395b184221b0ebbbb5b0de1bdd |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-5e6ca8395b184221b0ebbbb5b0de1bdd2025-01-24T13:39:53ZengMDPI AGMathematics2227-73902025-01-0113225110.3390/math13020251A Novel Prescribed-Time Convergence Acceleration Algorithm with Time RescalingXuehui Mei0Pengrui Zhang1Haijun Jiang2Zhiyong Yu3College of Mathematics and System Science, Xinjiang University, Urumqi 830047, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830047, ChinaSchool of Mathematics and Statistics, YiLi Normal University, Yining 835000, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi 830047, ChinaIn machine learning, the processing of datasets is an unavoidable topic. One important approach to solving this problem is to design some corresponding algorithms so that they can eventually converge to the optimal solution of the optimization problem. Most existing acceleration algorithms exhibit asymptotic convergence. In order to ensure that the optimization problem converges to the optimal solution within the prescribed time, a novel prescribed-time convergence acceleration algorithm with time rescaling is presented in this paper. Two prescribed-time acceleration algorithms are constructed by introducing time rescaling, and the acceleration algorithms are used to solve unconstrained optimization problems and optimization problems containing equation constraints. Some important theorems are given, and the convergence of the acceleration algorithms is proven using the Lyapunov function method. Finally, we provide numerical simulations to verify the effectiveness and rationality of our theoretical results.https://www.mdpi.com/2227-7390/13/2/251exponential prescribed-time convergenceacceleration algorithmtime rescalingoptimization problemLyapunov function |
| spellingShingle | Xuehui Mei Pengrui Zhang Haijun Jiang Zhiyong Yu A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling Mathematics exponential prescribed-time convergence acceleration algorithm time rescaling optimization problem Lyapunov function |
| title | A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling |
| title_full | A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling |
| title_fullStr | A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling |
| title_full_unstemmed | A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling |
| title_short | A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling |
| title_sort | novel prescribed time convergence acceleration algorithm with time rescaling |
| topic | exponential prescribed-time convergence acceleration algorithm time rescaling optimization problem Lyapunov function |
| url | https://www.mdpi.com/2227-7390/13/2/251 |
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